Finite Group Databasebeta

← #11861109

Subgroups — #11861109

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 643 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64116C211yesmaximal, characteristic, complemented
2#10594795C211yesmaximal, characteristic
3C2×#63815C211yesmaximal, characteristic, complemented
4C3×#5139C211yesmaximal, characteristic, complemented
5C3×#5124C211yesmaximal, characteristic, complemented
6#10591113C211yesmaximal, characteristic, complemented
7#10591057C211yesmaximal, characteristic, complemented
8#10590978C214yesmaximal, complemented
9#10590977C214yesmaximal, complemented
10#79257—31nomaximal
11#78989—31nomaximal
12C2×#3828C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16#64116—21no—
17#64116—21no—
18#64116C2212yescomplemented
19#64116C2212yescomplemented
20C2×#3743—21no—
21C2×C8×C3⋊D3—21no—
22C3×#926C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25#63833C412yescomplemented
26#63831C412yescomplemented
27#63830C412yescomplemented
28#63829C2214yes—
29#63825C412yescomplemented
30C2×#3711—21no—
31#63815—21no—
32#63815—21no—
33#63815C2212yescomplemented
34#63815C2212yescomplemented
35C2×D3×C3⋊C8—21no—
36C3×#825C2214yescomplemented
37C3×#822C2214yescomplemented
38#63570C2214yescomplemented
39#63554C2212yescomplemented
40Dic3×C3⋊C8C2212yescomplemented
41#5822—31no—
42C2×#948—31no—
43#5748—31no—
44C2×#907—31no—
45C2×#907—31no—
46C2×#907—31no—
47C2×#907—61no—
48C3×#430—31no—
49C3×#421—31no—
50#5139—31no—
51#5139D311yescharacteristic, complemented
52#5124D311yescharacteristic, complemented
53#5122—31no—
54#5005—31no—
55#4997—31no—
56#4895—34no—
57#4894—34no—
58#4824—34no—
59#4823—34no—
60C22×C32×C4C2311yescharacteristic
61C2×#638—21no—
62#3828—21no—
63#3828—21no—
64#3828C2×C412yes—
65#3828C2312yes—
66C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634C2×C411yescharacteristic
69C2×C3×#67—21no—
70C3×#235—21no—
71C3×#235—21no—
72C3×#235C2×C412yes—
73C3×#235C2312yes—
74C2×C3×D12C2×C411yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×Dic6C2×C411yescharacteristic
77C32×M16—21no—
78C32×M16C2312yes—
79C2×C32×C8—21no—
80C2×C3⋊(C3⋊C8)D411yescharacteristic
81C2×C3⋊(C3⋊C8)D411yescharacteristic
82C2×C3⋊(C3⋊C8)D411yescharacteristic
83C2×C3⋊(C3⋊C8)D411yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86#3743—22no—
87#3743—22no—
88C8×C3⋊D3—22no—
89C8×C3⋊D3—22no—
90C3×#217—21no—
91C3×C4⋊Dic3—21no—
92C3×C4×Dic3C2312yes—
93C3×#208—21no—
94C3×#208C2×C412yes—
95C3×#208C2×C412yes—
96C3×#208C2312yes—
97C2×C3×C3⋊C8—21no—
98C2×C3×C3⋊C8C2312yes—
99#3719C2×C414yes—
100#3717C2×C414yes—
101#3716C2×C414yes—
102#3714C2×C414yes—
103#3711—22no—
104#3711—22no—
105D3×C3⋊C8—22no—
106D3×C3⋊C8—22no—
107#2955—91noSylow
108C2×C3×#41—31no—
109C2×#235—31no—
110C2×#235—31no—
111C2×#235—61no—
112C2×#235C2×D311yescharacteristic
113C2×C3×M16—21no—
114C2×C3×M16—31no—
115C2×C3×M16—31no—
116C2×C3×M16C2×D311yescharacteristic
117C2×C3×M16C2×D311yescharacteristic
118C3×#117—31no—
119#951—32no—
120#950—34no—
121#949—32no—
122#948—32no—
123#948—32no—
124#948—61no—
125#948—61no—
126#942—32no—
127#932—32no—
128#926C2×D311yescharacteristic
129C2×#208—61no—
130C2×#208C2×D311yescharacteristic
131C2×#208C2×D311yescharacteristic
132C22×C3⋊C8—31no—
133C22×C3⋊C8—31no—
134C22×C3⋊C8—61no—
135C22×C3⋊C8—61no—
136#909—32no—
137#909—32no—
138#908—32no—
139#908—32no—
140#907—32no—
141#907—32no—
142#907—32no—
143#907—32no—
144#907—32no—
145#907—32no—
146#907—62no—
147#907—62no—
148#907—61no—
149#907—61no—
150#907—61no—
151#907—61no—
152#907—61no—
153#907—61no—
154#907—62no—
155#907—62no—
156#904—34no—
157C2×ΓL(1,𝔽25)—61no—
158C2×ΓL(1,𝔽25)—61no—
159C2×ΓL(1,𝔽25)—61no—
160C2×ΓL(1,𝔽25)—62no—
161C2×D3×C8—61no—
162C2×D3×C8—61no—
163C2×D3×C8—61no—
164C2×D3×C8—62no—
165C3×#108—34no—
166C3×#104—34no—
167#825—34no—
168#825C2×D314yescomplemented
169#822C2×D314yescomplemented
170#815—32no—
171C8×Dic3—32no—
172#805—34no—
173#803—32no—
174C4×C3⋊C8—32no—
175C23×C32#4111yescharacteristic
176C22×C3⋊D3—21no—
177C22×C3×D3—21no—
178C2×C32×C4C22×C411yescharacteristic
179C2×C32×C4C22×C411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4#4111yescharacteristic
183C2×C32×C4C2411yescharacteristic
184#638—22no—
185#638—22no—
186C2×C3⋊Dic3—21no—
187C4⋊(C3⋊D3)—21no—
188C4⋊(C3⋊D3)C22×C412yes—
189C4×C3⋊D3—22no—
190C4×C3⋊D3—22no—
191#634—21no—
192#634C22×C412yes—
193C3×#67—22no—
194C3×#67—22no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—22no—
197C3×D12—21no—
198C3×D12C22×C412yes—
199C3×C4×D3—22no—
200C3×C4×D3—22no—
201C3×Dic6—21no—
202C3×Dic6C22×C412yes—
203C32×C8—22no—
204C3⋊(C3⋊C8)C2×D411yescharacteristic
205C3⋊(C3⋊C8)C2×D411yescharacteristic
206C3⋊(C3⋊C8)C2×D411yescharacteristic
207C3⋊(C3⋊C8)C2×D411yescharacteristic
208C3×C3⋊C8—22no—
209C3×C3⋊C8C22×C414yes—
210#575—91no—
211C2×#131—91no—
212C2×#131—91no—
213#444—94no—
214#443—94no—
215#430—31no—
216#421—31no—
217#421—91no—
218#405—91no—
219C3×#41—32no—
220C3×#41—32no—
221C3×#41—61no—
222C3×#41—61no—
223C2×C3×Q8—31no—
224C2×C3×D4—31no—
225C2×C3×D4—61no—
226C22×C3×C4—21no—
227C22×C3×C4—61no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C2×#67—21no—
231C2×#67—62no—
232C2×#67—61no—
233C2×#67—61no—
234#235—21no—
235#235—21no—
236#235—32no—
237#235—32no—
238#235—32no—
239#235—32no—
240#235—62no—
241#235—62no—
242#235—62no—
243#235—62no—
244#235—61no—
245#235—61no—
246#235—61no—
247#235—61no—
248#235C4×D312yes—
249#235C22×D312yes—
250C2×D12—31no—
251C2×D12—31no—
252C2×D12—61no—
253C2×D12C4×D311yescharacteristic
254C2×C4×D3—21no—
255C2×C4×D3—62no—
256C2×C4×D3—61no—
257C2×C4×D3—61no—
258C2×Dic6—31no—
259C2×Dic6—31no—
260C2×Dic6—61no—
261C2×Dic6C4×D311yescharacteristic
262C3×M16—22no—
263C3×M16—21no—
264C3×M16—21no—
265C3×M16—22no—
266C3×M16—32no—
267C3×M16—32no—
268C3×M16—32no—
269C3×M16—61no—
270C3×M16C22×D312yes—
271C3×M16C22×D312yes—
272C2×C3×C8—22no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—32no—
276C2×C3×C8—61no—
277C3×C4⋊C4—61no—
278C3×C22⋊C4—61no—
279C3×C42—32no—
280#217—21no—
281#216—34no—
282#215—34no—
283#214—34no—
284#213—34no—
285C4⋊Dic3—21no—
286C4×Dic3C22×D312yes—
287#208—21no—
288#208—62no—
289#208—62no—
290#208C4×D312yes—
291#208C4×D312yes—
292#208C22×D312yes—
293C2×C3⋊C8—21no—
294C2×C3⋊C8—31no—
295C2×C3⋊C8—31no—
296C2×C3⋊C8—31no—
297C2×C3⋊C8—31no—
298C2×C3⋊C8—31no—
299C2×C3⋊C8—31no—
300C2×C3⋊C8—31no—
301C2×C3⋊C8—31no—
302C2×C3⋊C8—31no—
303C2×C3⋊C8—31no—
304C2×C3⋊C8—31no—
305C2×C3⋊C8—31no—
306C2×C3⋊C8—61no—
307C2×C3⋊C8—61no—
308C2×C3⋊C8—61no—
309C2×C3⋊C8—61no—
310C2×C3⋊C8—61no—
311C2×C3⋊C8—61no—
312C2×C3⋊C8—62no—
313C2×C3⋊C8—62no—
314C2×C3⋊C8C22×D312yes—
315Dic12—34no—
316D24—34no—
317#204—34no—
318#204—34no—
319ΓL(1,𝔽25)—62no—
320ΓL(1,𝔽25)—62no—
321ΓL(1,𝔽25)—62no—
322ΓL(1,𝔽25)—62no—
323ΓL(1,𝔽25)—62no—
324ΓL(1,𝔽25)—62no—
325ΓL(1,𝔽25)—64no—
326ΓL(1,𝔽25)—64no—
327D3×C8—62no—
328D3×C8—62no—
329D3×C8—62no—
330D3×C8—62no—
331D3×C8—62no—
332D3×C8—62no—
333D3×C8—64no—
334D3×C8—64no—
335C22×C32—41no—
336C22×C32C4×D411yescharacteristic
337C22×C32C4×D411yescharacteristic
338C22×C32C2×#4111yescharacteristic
339C2×C3⋊D3—22no—
340C2×C3⋊D3—42no—
341C2×C3×D3—22no—
342C2×C3×D3—42no—
343C32×C4C4×D411yescharacteristic
344C32×C4C4×D411yescharacteristic
345C32×C4C23×C411yescharacteristic
346C32×C4C22×D411yescharacteristic
347C3⋊Dic3—22no—
348C3×Dic3—22no—
349C3×Dic3—42no—
350C2×#41—31no—
351C2×#41—91no—
352#137—92no—
353#137—92no—
354AGL(1,ℤ/8)—92no—
355AGL(1,ℤ/8)—92no—
356#135—94no—
357#131—92no—
358#131—92no—
359#131—92no—
360#131—92no—
361#131—181no—
362#131—181no—
363#131—181no—
364#131—181no—
365C2×M16—31no—
366C2×M16—31no—
367C2×M16—181no—
368C2×M16—181no—
369C2×M16D3211yescharacteristic
370C22×C8—91no—
371C22×C8—181no—
372C22×C8—181no—
373#117—31no—
374#108—34no—
375#104—34no—
376#104—94no—
377#97—92no—
378C4×C8—92no—
379C23×C3—21no—
380C23×C3—61no—
381C23×C3#23711yescharacteristic
382C23×C3#23911yescharacteristic
383C22×D3—21no—
384C22×D3—62no—
385C22×D3—61no—
386C22×D3—61no—
387C3×Q8—32no—
388C3×Q8—61no—
389C3×D4—32no—
390C3×D4—62no—
391C3×D4—62no—
392C3×D4—61no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—61no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4C2×C4×D311yescharacteristic
404C2×C3×C4C2×C4×D311yescharacteristic
405C2×C3×C4C2×C4×D311yescharacteristic
406C2×C3×C4C2×C4×D311yescharacteristic
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4#23711yescharacteristic
412C2×C3×C4#23911yescharacteristic
413C2×C3×C4C23×D311yescharacteristic
414C2×C3×C4C23×D311yescharacteristic
415#67—22no—
416#67—22no—
417#67—64no—
418#67—64no—
419#67—62no—
420#67—62no—
421#67—62no—
422#67—62no—
423C2×Dic3—21no—
424C2×Dic3—22no—
425C2×Dic3—62no—
426C2×Dic3—61no—
427C2×Dic3—61no—
428D12—21no—
429D12—32no—
430D12—32no—
431D12—62no—
432D12—62no—
433D12—61no—
434D12—61no—
435D12C2×C4×D312yes—
436C4×D3—22no—
437C4×D3—22no—
438C4×D3—64no—
439C4×D3—64no—
440C4×D3—62no—
441C4×D3—62no—
442C4×D3—62no—
443C4×D3—62no—
444Dic6—21no—
445Dic6—32no—
446Dic6—32no—
447Dic6—62no—
448Dic6—62no—
449Dic6—61no—
450Dic6—61no—
451Dic6C2×C4×D312yes—
452C3×C8—24no—
453C3×C8—22no—
454C3×C8—22no—
455C3×C8—34no—
456C3×C8—62no—
457C3⋊C8—22no—
458C3⋊C8—31no—
459C3⋊C8—31no—
460C3⋊C8—31no—
461C3⋊C8—31no—
462C3⋊C8—31no—
463C3⋊C8—31no—
464C3⋊C8—31no—
465C3⋊C8—31no—
466C3⋊C8—61no—
467C3⋊C8—61no—
468C3⋊C8—61no—
469C3⋊C8—61no—
470C3⋊C8C2×C4×D314yes—
471C2×C32—21no—
472C2×C32—21no—
473C2×C32—21no—
474C2×C32C2×C4×D411yescharacteristic
475C3⋊D3—42no—
476C3×D3—42no—
477#41—32no—
478#41—32no—
479#41—61no—
480#41—61no—
481#41—92no—
482#41—92no—
483#41—181no—
484#41—181no—
485C2×Q8—31no—
486C2×Q8—91no—
487C2×D4—31no—
488C2×D4—61no—
489C2×D4—91no—
490C2×D4—181no—
491C22×C4—61no—
492C22×C4—181no—
493C22×C4C2×D3211yescharacteristic
494Q16—94no—
495SD16—94no—
496SD16—94no—
497D8—94no—
498M16—21no—
499M16—32no—
500M16—32no—
501M16—32no—
502M16—61no—
503M16—182no—
504M16—182no—
505M16—182no—
506M16—182no—
507M16C2×D3212yes—
508C2×C8—21no—
509C2×C8—32no—
510C2×C8—61no—
511C2×C8—91no—
512C2×C8—91no—
513C2×C8—91no—
514C2×C8—91no—
515C2×C8—91no—
516C2×C8—91no—
517C2×C8—182no—
518C2×C8—182no—
519C2×C8—182no—
520C2×C8—182no—
521C4⋊C4—61no—
522C22⋊C4—61no—
523C42—32no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—41no—
528C22×C3—41no—
529C22×C3—42no—
530C22×C3—62no—
531C22×C3—122no—
532C22×C3#67⋊C411yescharacteristic
533C22×C3#67⋊C411yescharacteristic
534C22×C3#89311yescharacteristic
535C22×C3#89311yescharacteristic
536C22×C3C2×#23711yescharacteristic
537C22×C3C2×#23911yescharacteristic
538C2×D3—22no—
539C2×D3—42no—
540C2×D3—64no—
541C2×D3—62no—
542C2×D3—62no—
543C2×D3—124no—
544C2×D3—122no—
545C2×D3—122no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—21no—
549C3×C4—21no—
550C3×C4—62no—
551C3×C4—122no—
552C3×C4#67⋊C411yescharacteristic
553C3×C4#67⋊C411yescharacteristic
554C3×C4#89311yescharacteristic
555C3×C4#89311yescharacteristic
556C3×C4C22×C4×D311yescharacteristic
557C3×C4C22×C4×D311yescharacteristic
558C3×C4C2×D3×D411yescharacteristic
559C3×C4C2×D3×D411yescharacteristic
560Dic3—22no—
561Dic3—42no—
562Dic3—64no—
563Dic3—62no—
564Dic3—62no—
565C32#295511yescharacteristic, complemented, Sylow
566C23—61no—
567C23—181no—
568C23#379611yescharacteristic
569Q8—32no—
570Q8—61no—
571Q8—92no—
572Q8—181no—
573D4—32no—
574D4—62no—
575D4—62no—
576D4—61no—
577D4—92no—
578D4—182no—
579D4—182no—
580D4—181no—
581C2×C4—61no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—181no—
586C2×C4—182no—
587C2×C4—182no—
588C2×C4#379611yescharacteristic
589C2×C4C4×D3211yescharacteristic
590C2×C4C4×D3211yescharacteristic
591C2×C4#381111yescharacteristic
592C2×C4#381111yescharacteristic
593C2×C4C22×D3211yescharacteristic
594C8—22no—
595C8—34no—
596C8—62no—
597C8—91no—
598C8—91no—
599C8—91no—
600C8—91no—
601C2×C3—22no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—41no—
610C2×C3—41no—
611C2×C3—122no—
612C2×C3C2×#67⋊C411yescharacteristic
613C2×C3C2×#89311yescharacteristic
614D3—42no—
615D3—124no—
616D3—122no—
617D3—122no—
618C22—41no—
619C22—62no—
620C22—122no—
621C22—182no—
622C22—362no—
623C22#6388111yescharacteristic
624C22#6388111yescharacteristic
625C22C2×#379611yescharacteristic
626C4—62no—
627C4—122no—
628C4—182no—
629C4#6388111yescharacteristic
630C4#6388111yescharacteristic
631C4C2×C4×D3211yescharacteristic
632C4C2×#381111yescharacteristic
633C3—21no—
634C3#7898911yescharacteristic, complemented
635C3#7925711yescharacteristic, complemented
636C2—21no—
637C2—21no—
638C2—21no—
639C2—122no—
640C2—362no—
641C2C2×#6388111yescharacteristic
subgroupG/H
centerC4C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC2×C32C2×C4×D4
prime radical#10594795C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2955
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#64116C2semidirect
3. C2×#63815C2semidirect
4. C3×#5139C2semidirect
5. C3×#5124C2semidirect
6. #10591113C2semidirect
7. #10591057C2semidirect
8. #10590978C2semidirect
9. #10590977C2semidirect
18. #64116C22semidirect
19. #64116C22semidirect
25. #63833C4semidirect
26. #63831C4semidirect
27. #63830C4semidirect
29. #63825C4semidirect
33. #63815C22semidirect
34. #63815C22semidirect
36. C3×#825C22semidirect
37. C3×#822C22semidirect
38. #63570C22semidirect
39. #63554C22semidirect
40. Dic3×C3⋊C8C22semidirect
51. #5139D3semidirect
52. #5124D3semidirect
168. #825C2×D3semidirect
169. #822C2×D3semidirect
565. C32#2955semidirect
634. C3#78989semidirect
635. C3#79257semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#641162
#105947952
C2×#638152
C3×#51392
C3×#51242
#105911132
#105910572
#105909782
#105909772
#792573
#789893